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Integrate each of the given functions.$$\int \frac{12 d x}{64+x^{2}}$$

$\frac{3}{2} \tan ^{-1}\left(\frac{x}{8}\right)+C$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 6

Inverse Trigonometric Forms

Integrals

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Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:25

Use substitution to find e…

01:44

Evaluate the following int…

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01:07

Find each integral.$$-…

04:52

$$\text {Evaluate the foll…

01:00

Find each integral.$$\…

01:14

Evaluate each definite int…

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01:17

we want to integrate the following expression, the integral of 12 X divided by 64 plus X square. This question is challenging our knowledge and ability to utilize integration techniques that we picked up throughout our journey. And single variable calculus in particular is testing our newfound knowledge of. The integral is known as inverse trig and metric integral. There are two inverse trig integral that are relevant. That I listen here the first and the last state of the integral. D'you over a squared minus U squared arsenio over a plus. See the second on the rights of the integral. D'you over A squared plus B squared is one over a R candidate over a plus C. We see that are integral is in the form to best if we identify you, do you end A. We can easily solve. So for a reason. Year old two we see that U. Is equal to X. Do you equal D. S. A. Is equal to route 64 or eight. Thus we can plug into our solution for equation to which means are integral is 12 integral dX 6/64 plus X squared, or 12/8 are tangent, X ray plus C. Or three. House are tangent X over eight plus C.

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